Multivariate data, particularly data having more than three attributes, is pervasive not only in engineering, science, and business, but also, thanks to the Internet, in everyday life. A simple example is the consideration of purchasing an automobile. Not only are there large numbers of makes, models, and types of automobiles, but each automobile has its own set of attributes, such as size, horsepower, fuel economy, fuel type. Unless a prospective purchaser has an allegiance to a particular manufacturer and/or model or otherwise is set on purchasing a specific vehicle, the purchaser can be overwhelmed by making a purchasing decision on any desired subset of attributes because of the large number automobiles that can be compared with one another. Various visualization schemes have been developed to assist users in understanding multivariate data in small to moderately sized data sets. However, each of these schemes has one or more limitations, including being limited to specific types of data sets, not being intuitive, and lacking repeatability, among others.